Question: Simplify the following expression: $ p = \dfrac{8x - 7}{-3} - \dfrac{-6}{7} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{8x - 7}{-3} \times \dfrac{7}{7} = \dfrac{56x - 49}{-21} $ Multiply the second expression by $\dfrac{-3}{-3}$ $ \dfrac{-6}{7} \times \dfrac{-3}{-3} = \dfrac{18}{-21} $ Therefore $ p = \dfrac{56x - 49}{-21} - \dfrac{18}{-21} $ Now the expressions have the same denominator we can simply subtract the numerators: $p = \dfrac{56x - 49 - 18 }{-21} $ Distribute the negative sign: $p = \dfrac{56x - 49 - 18}{-21}$ $p = \dfrac{56x - 67}{-21}$ Simplify the expression by dividing the numerator and denominator by -1: $p = \dfrac{-56x + 67}{21}$